Abbas, MujahidAlfuraidan, Monther RashedKhan, Abdul RahimNazir, Talat2015-12-042015-12-042015Abbas, M, Alfuraidan, MR, Khan, AR & Nazir, T 2015, 'Fixed point results for set-contractions on metric spaces with a directed graph', Fixed Point Theory and Applications, vol. 2015, art. 14, pp. 1-91687-1820 (print)1687-1812 (online)http://dx.doi.org/10.1186/s13663-015-0263-zhttp://hdl.handle.net/2263/51066In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complement various known comparable results in the literature.en© 2015 Abbas et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).Fixed pointSet-valued mappingSet-valued domainDirected graphGraph φ-contractionArticle